Mode-locked multi-mode fiber laser pulse source

ABSTRACT

A laser utilizes a cavity design which allows the stable generation of high peak power pulses from mode-locked multi-mode fiber lasers, greatly extending the peak power limits of conventional mode-locked single-mode fiber lasers. Mode-locking may be induced by insertion of a saturable absorber into the cavity and by inserting one or more mode-filters to ensure the oscillation of the fundamental mode in the multi-mode fiber. The probability of damage of the absorber may be minimized by the insertion of an additional semiconductor optical power limiter into the cavity. To amplify and compress optical pulses in a multi-mode (MM) optical fiber, a single-mode is launched into the MM fiber by matching the modal profile of the fundamental mode of the MM fiber with a diffraction-limited optical mode at the launch end, The fundamental mode is preserved in the MM fiber by minimizing mode-coupling by using relatively short lengths of step-index MM fibers with a few hundred modes and by minimizing fiber perturbations. Doping is confined to the center of the fiber core to preferentially amplify the fundamental mode, to reduce amplified spontaneous emission and to allow gain-guiding of the fundamental mode. Gain-guiding allows for the design of systems with length-dependent and power-dependent diameters of the fundamental mode. To allow pumping with high-power laser diodes, a double-clad amplifier structure is employed. For applications in nonlinear pulse-compression, self phase modulation and dispersion in the optical fibers can be exploited. High-power optical pulses may be linearly compressed using bulk optics dispersive delay lines or by chirped fiber Bragg gratings written directly into the SM or MM optical fiber. High-power cw lasers operating in a single near-diffraction-limited mode may be constructed from MM fibers by incorporating effective mode-filters into the laser cavity. Regenerative fiber amplifiers may be constructed from MM fibers by careful control of the recirculating mode. Higher-power Q-switched fiber lasers may be constructed by exploiting the large energy stored in MM fiber amplifiers.

RELATED APPLICATIONS

This application is a continuation application of U.S. application Ser.No. 10/424,220 filed Apr. 25, 2003, which is a continuation applicationof U.S. application Ser. No. 09/785,944 filed Feb. 16, 2001, which is acontinuation application of U.S. application Ser. No. 09/199,728 filedNov. 25, 1998, now U.S. Pat. No. 6,275,512 issued Aug. 14, 2001.

FIELD OF THE INVENTION

The present invention relates to the amplification of single mode lightpulses in multi-mode fiber amplifiers, and more particularly to the useof multi-mode amplifying fibers to increase peak pulse power in amode-locked laser pulse source used for generating ultra-short opticalpulses.

The present invention relates to the use of multi-mode fibers foramplification of laser light in a single-mode amplifier system.

BACKGROUND OF THE INVENTION

1. Background Relating to Optical Amplifiers

Single-mode rare-earth-doped optical fiber amplifiers have been widelyused for over a decade to provide diffraction-limited opticalamplification of optical pulses. Because single mode fiber amplifiersgenerate very low noise levels, do not induce modal dispersion, and arecompatible with single mode fiber optic transmission lines, they havebeen used almost exclusively in telecommunication applications.

The amplification of high peak-power pulses in a diffraction-limitedoptical beam in single-mode optical fiber amplifiers is generallylimited by the small fiber core size that needs to be employed to ensuresingle-mode operation of the fiber. In general the onset ofnonlinearities such as self-phase modulation lead to severe pulsedistortions once the integral of the power level present inside thefiber with the propagation length exceeds a certain limiting value. Fora constant peak power P inside the fiber, the tolerable amount ofself-phase modulation Φ_(nl) is given by${\Phi_{nl} = {\frac{2\pi\quad n_{2}{PL}}{\lambda\quad A} \leq 5}},$where A is the area of the fundamental mode in the fiber, ë is theoperation wavelength, L is the fiber length and n₂=3.2×10⁻²⁹ m²/W is thenonlinear refractive index in silica optical fibers.

As an alternative to single-mode amplifiers, amplification in multi-modeoptical fibers has been considered. However, in general, amplificationexperiments in multi-mode optical fibers have led tonon-diffraction-limited outputs as well as unacceptable pulse broadeningdue to modal dispersion, since the launch conditions into the multi-modeoptical fiber and mode-coupling in the multi-mode fiber have not beencontrolled.

Amplified spontaneous emission in a multi-mode fiber has been reduced byselectively exciting active ions close to the center of the fiber coreor by confining the active ions to the center of the fiber core. U.S.Pat. No. 5,187,759, hereby incorporated herein by reference. Since theoverlap of the low-order modes in a multi-mode optical fiber is highestwith the active ions close to the center of the fiber core, anyamplified spontaneous emission will then also be predominantly generatedin low-order modes of the multi-mode fiber. As a result, the totalamount of amplified spontaneous emission can be reduced in themulti-mode fiber, since no amplified spontaneous emission is generatedin high-order modes.

As an alternative for obtaining high-power pulses, chirped pulseamplification with chirped fiber Bragg gratings has been employed. Oneof the limitations of this technique is the relative complexity of theset-up.

More recently, the amplification of pulses to peak powers higher than 10KW has been achieved in multi-mode fiber amplifiers. See U.S. Pat. No.5,818,630, entitled Single-Mode Amplifiers and Compressors Based onMulti-Mode Fibers, assigned to the assignee of the present invention,and hereby incorporated herein by reference. As described therein, thepeak power limit inherent in single-mode optical fiber amplifiers isavoided by employing the increased area occupied by the fundamental modewithin multi-mode fibers. This increased area permits an increase in theenergy storage potential of the optical fiber amplifier, allowing higherpulse energies before the onset of undesirable nonlinearities and gainsaturation. To accomplish this, that application describes theadvantages of concentration of the gain medium in the center of themulti-mode fiber so that the fundamental mode is preferentiallyamplified. This gain-confinement is utilized to stabilize thefundamental mode in a fiber with a large cross section by gain guiding.

Additionally, that reference describes the writing of chirped fiberBragg gratings onto multi-mode fibers with reduced mode-coupling toincrease the power limits for linear pulse compression of high-poweroptical pulses. In that system, double-clad multi-mode fiber amplifiersare pumped with relatively large-area high-power semiconductor lasers.Further, the fundamental mode in the multi-mode fibers is excited byemploying efficient mode-filters. By further using multi-mode fiberswith low mode-coupling, the propagation of the fundamental mode inmulti-mode amplifiers over lengths of several meters can be ensured,allowing the amplification of high-power optical pulses in dopedmulti-mode fiber amplifiers with core diameters of several tens ofmicrons, while still providing a diffraction limited output beam. Thatsystem additionally employed cladding pumping by broad area diode arraylasers to conveniently excite multi-mode fiber amplifiers.

2. Background Relating to Mode-Locked Lasers

Both actively mode-locked lasers and passively mode-locked lasers arewell known in the laser art. For example, compact mode-locked lasershave been formed as ultra-short pulse sources using single-moderare-earth-doped fibers. One particularly useful fiber pulse source isbased on Kerr-type passive mode-locking. Such pulse sources have beenassembled using widely available standard fiber components to providepulses at the bandwidth limit of rare-earth fiber lasers with GigaHertzrepetition rates.

Semiconductor saturable absorbers have recently found applications inthe field of passively mode-locked, ultrashort pulse lasers. Thesedevices are attractive since they are compact, inexpensive, and can betailored to a wide range of laser wavelengths and pulsewidths. Quantumwell and bulk semiconductor saturable absorbers have also been used tomode-lock color center lasers

A saturable absorber has an intensity-dependent loss l. The single passloss of a signal of intensity I through a saturable absorber ofthickness d may be expressed asl−1−exp(−αd)in which α is the intensity dependent absorption coefficient given by:α(I)−α₀/(1+I/I_(SAT))Here α₀ is the small signal absorption coefficient, which depends uponthe material in question. I_(SAT) is the saturation intensity, which isinversely proportional to the lifetime (τ_(A)) of the absorbing specieswithin the saturable absorber. Thus, saturable absorbers exhibit lessloss at higher intensity.

Because the loss of a saturable absorber is intensity dependent, thepulse width of the laser pulses is shortened as they pass through thesaturable absorber. How rapidly the pulse width of the laser pulses isshortened is proportional to |dq₀/dI|, in which q₀ is the nonlinearloss:q ₀ =l/(I)−l(I=0)l(I=0) is a constant (=1−exp(α₀d)) and is known as the insertion loss.As defined herein, the nonlinear loss q₀ of a saturable absorberdecreases (becomes more negative) with increasing intensity I. |dq₀/dI|stays essentially constant until I approaches I_(SAT), becomingessentially zero in the bleaching regime, i.e., when I>>I_(SAT).

For a saturable absorber to function satisfactorily as a mode-lockingelement, it should have a lifetime (i.e., the lifetime of the upperstate of the absorbing species), insertion loss l(I=0), and nonlinearloss q₀ appropriate to the laser. Ideally, the insertion loss should below to enhance the laser's efficiency, whereas the lifetime and thenonlinear loss q₀ should permit self-starting and stable cwmode-locking. The saturable absorber's characteristics, as well as lasercavity parameters such as output coupling fraction, residual loss, andlifetime of the gain medium, all play a role in the evolution of a laserfrom startup to mode-locking.

As with single-mode fiber amplifiers, the peak-power of pulses frommode-locked single-mode lasers has been limited by the small fiber coresize that has been employed to ensure single-mode operation of thefiber. In addition, in mode-locked single-mode fiber lasers, theround-trip nonlinear phase delay also needs to be limited to around ∂ toprevent the generation of pulses with a very large temporally extendedbackground, generally referred to, as a pedestal. For a standardmode-locked single-mode erbium fiber laser operating at 1.55 μm with acore diameter of 10 μm and a round-trip cavity length of 2 m,corresponding to a pulse repetition rate of 50 MHz, the maximumoscillating peak power is thus about 1 KW.

The long-term operation of mode-locked single-mode fiber lasers isconveniently ensured by employing an environmentally stable cavity asdescribed in U.S. Pat. No. 5,689,519, entitled Environmentally StablePassively Mode-locked Fiber Laser Pulse Source, assigned to the assigneeof the present invention, and hereby incorporated herein by reference.The laser described in this reference minimizes environmentally inducedfluctuations in the polarization state at the output of the single-modefiber. In the described embodiments, this is accomplished by including apair of Faraday rotators at opposite ends of the laser cavity tocompensate for linear phase drifts between the polarization eigenmodesof the fiber.

Recently the reliability of high-power single-mode fiber laserspassively mode-locked by saturable absorbers has been greatly improvedby implementing non-linear power limiters by insertion of appropriatesemiconductor two-photon absorbers into the cavity, which minimizes thepeak power of the damaging Q-switched pulses often observed in thestart-up of mode-locking and in the presence of misalignments of thecavity. See U.S. patent application Ser. No. 09/149,369, filed on Sep.8, 1998, entitled Resonant Fabry-Perot Semiconductor Saturable Absorbersand Two-Photon Absorption Power Limiters, assigned to the assignee ofthe present invention, and hereby incorporated herein by reference.

To increase the pulse energy available from mode-locked single-modefiber lasers the oscillation of chirped pulses inside the laser cavityhas been employed. M. Hofer et al., Opt. Lett., vol. 17, page 807-809.As a consequence the pulses are temporally extended, giving rise to asignificant peak power reduction inside the fiber laser. However, thepulses can be temporally compressed down to approximately the bandwidthlimit outside the laser cavity. Due to the resulting high peak power,bulk-optic dispersive delay lines have to be used for pulse compression.For neodymium fiber lasers, pulse widths of the order of 100 fs can beobtained.

The pulse energy from mode-locked single-mode fiber lasers has also beenincreased by employing chirped fiber gratings. The chirped fibergratings have a large amount of negative dispersion, broadening thepulses inside the cavity dispersively, which therefore reduces theirpeak power and also leads to the oscillation of high-energy pulsesinside the single-mode fiber lasers.

See U.S. Pat. No. 5,450,427, entitled Technique for the Generation ofOptical Pulses in Mode-Locked Lasers by Dispersive Control of theOscillation Pulse Width, and U.S. Pat. No. 5,627,848, entitled Apparatusfor Producing Femtosecond and Picosecond Pulses from Fiber LasersCladding Pumped with Broad Area Diode Laser Arrays, both of which areassigned to the assignee of the present invention and herebyincorporated herein by reference. In these systems, the generated pulsesare bandwidth-limited, though the typical oscillating pulse widths areof the order of a few ps.

However, though the dispersive broadening of the pulse width oscillatinginside a single-mode fiber laser cavity does increase the oscillatingpulse energy compared to a ‘standard’ soliton fiber laser, it does notincrease the oscillating peak power. The maximum peak power generatedwith these systems directly from the fiber laser is still limited toaround I KW.

Another highly integratable method for increasing the peak power ofmode-locked lasers is based on using chirped periodically poled LiNbO₃(chirped PPLN). Chirped PPLN permits simultaneous pulse compression andfrequency doubling of an optically chirped pulse. See U.S. patentapplication Ser. No. 08/845,410, filed on Apr. 25, 1997, entitled Use ofAperiodic Quasi-Phase-Matched Gratings in Ultrashort Pulse Sources,assigned to the assignee of the present application, and herebyincorporated herein by reference. However, for chirped PPLN to producepulse compression from around 3 ps to 300 fs and frequency doubling withhigh conversion efficiencies, generally peak powers of the order ofseveral KW are required. Such high peak powers are typically outside therange of mode-locked single-mode erbium fiber lasers.

Broad area diode laser arrays have been used for pumping of mode-lockedsingle-mode fiber lasers, where very compact cavity designs werepossible. The pump light was injected through a V-groove from the sideof double-clad fiber, a technique typically referred to as side-pumping.However, such oscillator designs have also suffered from peak powerlimitations due to the single-mode structure of the oscillator fiber.

It has also been suggested that a near diffraction-limited output beamcan be obtained from a multi-mode fiber laser when keeping the fiberlength shorter than 15 mm and selectively providing a maximum amount offeedback for the fundamental mode of the optical fiber. “Efficient laseroperation with nearly diffraction-limited output from a diode-pumpedheavily Nd-doped multi-mode fiber”, Optics Letters, Vol. 21, pp. 266-268(1996) hereby incorporated herein by reference. In this technique,however, severe mode-coupling has been a problem, as the employedmulti-mode fibers typically support thousands of modes. Also, only anair-gap between the endface of the multi-mode fiber and a laser mirrorhas been suggested for mode-selection. Hence, only very poor modaldiscrimination has been obtained, resulting in poor beam quality.

While the operation of optical amplifiers, especially in the presence oflarge seed signals, is not very sensitive to the presence of spuriousreflections, the stability of mode-locked lasers critically depends onthe minimization of spurious reflections. Any stray reflections producesub-cavities inside an oscillator and result in injection signals forthe cw operation of a laser cavity and thus prevent the onset ofmode-locking. For solid-state Fabry-Perot cavities a suppression ofintra-cavity reflections to a level <<1% (in intensity) is generallybelieved to be required to enable the onset of mode-locking.

The intra-cavity reflections that are of concern in standard mode-lockedlasers can be thought of as being conceptually equivalent tomode-coupling in multi-mode fibers. Any mode-coupling in multi-modefibers clearly also produces a sub-cavity with a cw injection signalproportional to the amount of mode-coupling. However, the suppression ofmode-coupling to a level of <<I% at any multi-mode fiber discontinuitiesis very difficult to achieve. Due to optical aberrations, even well-corrected optics typically allow the excitation of the fundamental modein multi-mode fibers only with maximum efficiency of about 95%.Therefore to date, it has been considered that mode-locking of amulti-mode fiber is impossible and no stable operation of a mode-lockedmulti-mode fiber laser has yet been demonstrated.

3. Description of the Related Art

Rare-earth-doped optical fibers have long been considered for use assources of coherent light, as evidenced by U.S. Pat. No. 3,808,549 toMaurer (1974), since their light-guiding properties allow theconstruction of uniquely simple lasers. However, early work on fiberlasers did not attract considerable attention, because no methods ofgenerating diffraction-limited coherent light were known. Man currentapplications of lasers benefit greatly from the presence of diffract onlimited light.

Only when it became possible to manufacture single-mode (SM)rare-earth-doped fibers, as reported by Poole et al. in “Fabrication ofLow-Loss Optical Fibres Containing Rare-Ear Ions”, Optics Letters, Vol.22, pp. 737-738 (1985), did the rare-earth-doped optical fibertechnology become viable. In this technique, only the fundamental modeof the optical fiber is guided at the lasing wavelength, thus ensuringdiffraction-limited output.

Driven by the needs of optical fiber telecommunications for SM opticalfiber amplifiers, nearly all further developments for more than a decadein this area were concentrated on perfecting SM fiber amplifiers. Inparticular, the motivation for developing SM fiber amplifiers stemmedfrom the fact that SM fiber amplifiers generate the least amount ofnoise and they are directly compatible with SM fiber optic transmissionlines. SM fiber amplifiers also have the highest optical transmissionbandwidths, since, due to the absence of any higher-order modes, modaldispersion is completely eliminated. In general, modal dispersion is themost detrimental effect limiting the transmission bandwidth ofmulti-mode (MM) optical fibers, since the higher-order modes, ingeneral, have different propagation constants.

However, in the amplification of short-optical pulses, the use of SMoptical fibers is disadvantageous, cause the limited core area limitsthe saturation energy of the optical fiber and thus the obtainable pulseenergy. The saturation energy of a laser amplifier can be expressed as${E_{sat} = \frac{h\quad\upsilon\quad A}{\sigma}},$where h is Planck's constant, υ is the optical frequency, a is thestimulated emission cross section and A is the core area. The highestpulse energy generated from a SM optical fiber to date is about 160 μJ(disclosed by Taverner et al. in Optics Letters, Vol. 22, pp. 378-380(1997), and was obtained from a SM erbium-doped fiber with a corediameter of 15 μm, which is about the largest core diameter that iscompatible with SM propagation at 1.55 μm. This result was obtained witha fiber numerical aperture of NA≈0.07. Any further increase in corediameter requires a further lowering of the NA of the fiber and resultsin an unacceptably high sensitivity to bend-losses.

As an alternative to SM amplifiers amplification in multi-mode (MM)optical fibers has been considered. See, for example, “Chirped-pulseamplification of ultrashort pulses with a multi-mode Tm:ZBLAN fiberupconversion amplifier” by Yang et al., Optics Letters, Vol. 20, pp.1044-1046 (1995). However, in general, amplification experiments in MMoptical fibers have led to non-diffraction-limited outputs as well asunacceptable pulse broadening due to modal dispersion, since the launchconditions into the MM optical fiber and mode-coupling in the MM fiberwere not controlled.

It was recently suggested by Griebner et al. in “‘Efficient laseroperation with nearly diffraction-limited output from a diode-pumpedheavily Nd-doped multi-mode fiber”, Optics Letters, Vol. 21, pp. 266-268(1996), that a near diffraction-limited output be can be obtained from aMM fiber laser when keeping the fiber length shorter than 15 mm andselectively providing a maximum amount of feedback for the fundamentalmode of the optical fiber. In this technique, however, severeode-coupling was a problem, as the employed MM fibers supported some10,000 modes. Also, only an air-gap between the endface of the MM fiberand a laser mirror was suggested for mode-selection. Hence, only verypoor modal discrimination was obtained, resulting in poor beam quality.

In U.S. Pat. No. 5,187,759 to DiGiovanni et al., it was suggested thatamplified spontaneous emission (ASE) in a MM fiber can be reduced byselectively exciting any active ions lose to the center of the fibercore or by confining the active ions to the center of the fiber core.Since the overlap of the low-order modes in a MM optical fiber ishighest with the active ions close to the center of the fiber core, anyASE will then also be predominantly generated in low-order modes of theMM fiber. As a result, the total amount of ASE can be greatly reduced inMM fiber, since no ASE is generated in high-order modes. However,DiGiovanni described dopant confinement only with respect to ASEreduction. DiGiovanni did not suggest that, in the presence ofmode-scattering, dopant confinement can enhance the beam quality of thefundamental mode of the M fiber under SM excitation. Also, the system ofDiGiovanni did not take into account the fact that gain-guiding inducedby dopant confinement can in fact effectively guide a fundamental modein a MM fiber. This further reduces ASE in MM fibers as well as allowingfor SM operation.

In fact, the system of DiGiovanni et al. is not very practical, since itconsiders a MM signal source, which leads to a non-diffraction-limitedoutput beam. Further, only a single cladding was considered for thedoped fiber, which is disadvantageous when trying to couple high-powersemi-conductor lasers into the optical fibers. To couple high-powersemiconductor lasers into MM fibers, a double-clad structure, assuggested in the above-mentioned patent to Maurer, can be of anadvantage.

To the inventors' knowledge, gain-guiding has not previously beenemployed in optical fibers. On the other hand, gain-guiding is wellknown in conventional semiconductor and solid-state lasers. See, forexample, “‘Alexandrite-laser-pumped Cr³⁺:Li rAlF₆” by Harter et al.,Optics Letters, Vol. 17, pp. 1512-1514 (1992). Indeed, in SM fibers,gain-guiding is irrelevant due to the strong confinement of thefundamental mode by the wave-guide structure. However, in MM opticalfibers., the confinement of the fundamental mode by the waveguidestructure becomes comparatively weaker, allowing for gain-guiding to setin. As the core size in a MM fiber becomes larger, light propagation inthe fiber structure tends to approximate free-space propagation. Thus,gain-guiding can be expected eventually to be significant, providedmode-coupling can be mad sufficiently small. In addition to providinghigh pulse energies, MM optical fiber amplifiers can also be used toamplify very high peak power pulses due to their increased fiber crosssection compared to SM fiber amplifiers. MM undoped fibers and MMamplifier fibers can also be used for pulse compression as recentlydisclosed by Fermann et al. in U.S. application Ser. No. 08/789,995(filed Jan. 28, 1997). However, this work was limited to the use of MMfibers as soliton Raman compressors in conjunction with a nonlinearspectral filtering action to clean-up the spectral profile, which maylimit the overall efficiency of the system.

Compared to pulse compression in SM fibers, such as that disclosed inU.S. Pat. No. 4,913,520 to Kafka et al., higher-pulse energies can beobtained in MM fibers due to the increased mode-size of the fiber. Inparticular, V-values higher than 2.5 and relatively high indexdifferences between core and cladding (i.e. a Δn>0.3%) can beeffectively employed. In “Generation of high-energy 10-fs pulses by anew pulse compression technique”, Conference on Lasers andElectro-Optics, CLEO 91, paper DTuR5, Optical Society of AmericaTechnical Digest Series, #9, pp. 189-190 (1996), M. Nisoli et al.suggested the use of hollow-core fibers for pulse-compression, ashollow-core fibers allow an increase in the mode size of the fundamentalmode. However, hollow-core fibers have an intrinsic transmission loss,they need to be filled with gas, and they need to be kept straight inorder to minimize the transmission losses, which makes them highlyimpractical.

As an alternative to obtaining high-power pulses, chirped pulseamplification with chirped fiber Bragg gratings may be employed, asdisclosed in U.S. Pat. No. 5,499,134 to Galvanauskas et al. (1996). Oneof the limitations of this technique is that, in the compressiongrating, a SM fiber with a limited core area is employed. Higher pulseenergies could be obtained by employing chirped fiber Bragg gratings inMM fibers with reduced mode-coupling for pulse compression. Indeed,unchirped fiber Bragg gratings were recently demonstrated in double-modefibers by Strasser et al. in “Reflective-mode conversion with UV-inducedphase gratings in two-mode fiber”, Optical Society of America Conferenceon Optical Fiber Communication, OFC97, pp. 348-349, (1997). However,these gratings were blazed to allow their use as mode-converters, i.e.,to couple the fundamental mode to a higher-order mode. The use of Bragggratings in pulse-compression calls for an unblazed grating to minimizethe excitation of any higher-order modes in reflection.

It has long been known that a SM signal can be coupled into a MM fiberstructure and preserved for propagation lengths of 100s of meters. See,for example, “Pulse Dispersion for Single-Mode Operation of Multi-modeCladded Optical Fibres”, Gambling et al., Electron. Lett., Vol. 10, pp.148-149, (1974) and “Mode conversion coefficients in optical fibers”,Gambling et al., Applied Optics, Vol. 14, pp. 1538-1542, (1975).However, Gambling et al. found low levels of mode-coupling only inliquid-core fibers. On the other hand, mode-coupling in MM solid-corefibers was found to be severe, allowing for the propagation of afundamental mode only in mm lengths of fiber. Indeed, as with the workby Griebner et al., Gambling et al. used MM solid-core optical fibersthat supported around 10,000 or more modes.

In related work, Gloge disclosed in “Optical Power Flow in Multi-modeFibers”, The Bell System Technical Journal, Vol. 51, pp. 1767-1783,(1972), the use of MM fibers that supported only 700 modes, wheremode-coupling was sufficiently reduced to allow SM propagation overfiber lengths of 10 cm.

However, it was not shown by Gloge that mode-coupling can be reduced byoperating MM fibers at long wavelengths (1.55 μm) and by reducing thetotal number of modes to less than 700. Also, in this work, the use ofMM fibers as amplifiers and the use of the nonlinear properties of MMfibers was not considered.

The inventors are not aware of any prior art using MM fibers to amplifySM signals where the output remains primarily in the fundamental mode,the primary reason being that amplification in MM fibers is typicallynot suitable for long-distance signal propagation as employed in theoptical telecommunication area. The inventors arc also not aware of anyprior art related to pulse compression in multi-mode fibers, where theoutput remains in the fundamental mode.

All of the above-mentioned articles, patents and patent applications arehereby incorporated herein by reference.

SUMMARY OF THE INVENTION

This invention overcomes the foregoing difficulties associated with peakpower limitations in mode-locked lasers, and provides a mode-lockedmulti-mode fiber laser.

This laser utilizes cavity designs which allow the stable generation ofhigh peak power pulses from mode-locked multi-mode fiber lasers, greatlyextending the peak power limits of conventional mode-locked single-modefiber lasers. Mode-locking may be induced by insertion of a saturableabsorber into the cavity and by inserting one or more mode-filters toensure the oscillation of the fundamental mode in the multi-mode fiber.The probability of damage of the absorber may be minimized by theinsertion of an additional semiconductor optical power limiter into thecavity. The shortest pulses may also be generated by taking advantage ofnonlinear polarization evolution inside the fiber. The long-termstability of the cavity configuration is ensured by employing anenvironmentally stable cavity. Pump light from a broad-area diode lasermay be delivered into the multi-mode fiber by employing acladding-pumping technique.

With this invention, a mode-locked fiber laser may be constructed toobtain, for example, 360 fsec near-bandwidth-limited pulses with anaverage power of 300 mW at a repetition rate of 66.7 MHz. The peak powerof these exemplary pulses is estimated to be about 6 KW.

It is an object of the present invention to increase the energy storagepotential in an optical fiber amplifier and to produce peak powers andpulse energies which are higher than those achievable in single-mode(SM) fibers before the onset of undesirable nonlinearities and gainsaturation.

Another object of the present invention is to achieve amplification ofthe fundamental mode within a multi-mode (MM) fiber while reducingamplified spontaneous emission (ASE).

A further object of the present invention is to employ gain-guidingwithin a MM fiber to improve the stability of the fundamental mode.

Yet another object of the present invention is to compress high peakpower pulses into the range of a few psec to a fsec while preserving anear diffraction-limited output.

To achieve the above objects, the present invention employs a multi-mode(MM) optical fiber in an optical amplification system. According to thepresent invention, MM optical fibers, i.e., fibers with a V-valuegreater than approximately 2.5, provide an output in the fundamentalmode. This allows the generation of much higher peak powers and pulseenergies compared to SM fibers before the onset of undesirablenonlinearities and gain saturation. The increased fiber cross sectionequally greatly increases the energy storage potential in an opticalfiber amplifier. The amplification system of the present invention isuseful in applications requiring ultrafast and high-power pulse sources.

According to one aspect of the present invention, the gain medium is inthe center of the MM fiber so that the fundamental mode ispreferentially amplified and spontaneous emission is reduced. Further,gain-confinement is used to stabilize the fundamental mode in a fiberwith a large cross section by gain guiding.

According to one embodiment of the present invention, the exploitationof self-phase modulation and other nonlinearities in (rare-earth) dopedor undoped MM fibers allows the compression of high peak power pulsesinto the range of a few fsec while a near diffraction-limited output ispre-served.

According to another embodiment of the present invention, by writingchirped fiber Bragg gratings into MM optical fibers with reducedmode-coupling, the power limits for linear pulse compression ofhigh-power optical pulses are greatly increased. Further, by employingdouble-clad MM fiber amplifiers, pumping with relatively large-areahigh-power semiconductor lasers is made possible.

According to yet another embodiment of the present invention, theincorporation of efficient mode-filters enables cw lasing in a neardiffraction-limited single mode from (rare-earth) doped MM opticalfibers.

According to yet another embodiment of the present invention, MM opticalfibers allow the construction of fiber optic regenerative amplifiers andhigh-power Q-switched lasers. Further, MM optical fibers allow thedesign of cladding-pumped fiber lasers using dopants with relativelyweak absorption cross sections.

These and other objects and features of the present invention will beapparent from the following detailed description of the preferredembodiments and the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

The following description of the preferred embodiments of the inventionreferences the appended drawings, in which like elements bear identicalreference numbers throughout.

FIG. 1 is a schematic illustration showing the construction of apreferred embodiment of the present invention which utilizes end-pumpingfor injecting pump light into the multi-mode fiber.

FIG. 2 is a graph showing the typical autocorrelation of pulsesgenerated by the invention of FIG. 1.

FIG. 3 is a graph showing the typical pulse spectrum generated by theinvention of FIG. 1.

FIG. 4 is a schematic illustration showing the construction of analternate preferred embodiment utilizing a side-pumping mechanism forinjecting pump light into the multi-mode fiber.

FIG. 5 is a schematic illustration of an alternative embodiment whichuses a length of positive dispersion fiber to introduce chirped pulsesinto the cavity.

FIG. 6 is a schematic illustration of an alternative embodiment whichuses chirped fiber gratings with negative dispersion in the laser cavityto produce high-energy, near bandwidth-limited pulses.

FIGS. 7 a and 7 b illustrate polarization-maintaining multi-mode fibercross sections which may be used to construct environmentally stablecavities in the absence of Faraday rotators.

FIG. 8 is a schematic illustration of an alternative embodiment whichutilizes one of the fibers illustrated in FIGS. 7 a and 7 b.

FIGS. 9 a, 9 b and 9 c illustrate the manner is which the fundamentalmode of the multi-mode fibers of the present invention may be matched tothe mode of a singe mode fiber. These include a bulk optic imagingsystem, as shown in FIG. 9 a, a multi-mode to single-mode splice, asshown in FIG. 9 b, and a tapered section of multi-mode fiber, asillustrated in FIG. 9 c.

FIG. 10 is a schematic illustration of an alternative embodiment inwhich a fiber grating is used to predominantly reflect the fundamentalmode of a multi-mode fiber.

FIG. 11 is a schematic illustration of an alternative embodiment inwhich active or active-passive mode-locking is used to mode-lock themulti-mode laser.

FIG. 12 is a diagrammatic view of a multi-mode fiber amplifier systemaccording to the first embodiment of the present invention.

FIG. 13 is a graph showing the coupling efficiency of a multi-modeamplifier fiber into a mode-filter fiber as a function of bend-radius ofthe multi-mode amplifier fiber.

FIG. 14 is a graph showing the autocorrelation of the amplified pulsesfrom a multi-mode amplifier fiber measured under optimum mode-matchconditions.

FIG. 15 is a graph showing the autocorrelation of the amplified pulsesfrom a multi-mode amplifier fiber measured under non-optimum mode-matchconditions.

FIG. 16 is a block diagram of a multi-mode fiber amplifier systemaccording to the second embodiment of the present invention.

FIG. 17 is a block diagram of a multi-mode fiber amplifier systemaccording to the third embodiment of the present invention, wherein apulse compressor is disposed at an output of the multi-mode fiber.

FIG. 18 is a diagrammatic view of a multi-mode fiber amplifier systemaccording to a fourth embodiment of the present invention.

FIG. 19 is a conceptual drawing of a fiber cross section employing adoped multi-mode fiber core and an undoped fiber cladding according to afifth embodiment of the present invention.

FIG. 20 is a diagrammatic view of a multi-mode fiber amplifier systemaccording to a sixth embodiment of the present invention, wherein afiber regenerative amplifier is constructed from a multi-mode fiberamplifier.

FIG. 21 is a diagrammatic view of a multi-mode fiber amplifier systemaccording to a seventh embodiment of the present invention, wherein a MMQ-switched fiber laser source is constructed.

FIG. 22 is a block diagram of a multi-mode fiber amplifier systemaccording to the eighth embodiment of the present invention, wherein apreamplifier is inserted before the multi-mode fiber.

FIG. 23 is a block diagram of a multi-mode fiber amplifier systemaccording to the ninth embodiment of the present invention, wherein afrequency converter is disposed at an output of the multi-mode fiber.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

FIG. 1A illustrates the mode-locked laser cavity 11 of this inventionwhich uses a length of multi-mode amplifying fiber 13 within the cavityto produce ultra-short, high-power optical pulses. As used herein,“ultra-short” means a pulse width below 100 ps. The fiber 13, in theexample shown, is a 1.0 m length of non-birefringent Yb³⁺/Er³⁺-dopedmulti-mode fiber. Typically, a fiber is considered multi-mode when theV-value exceeds 2.41, i.e., when modes in addition to the fundamentalmode can propagate in the optical fiber. This fiber is coiled onto adrum with a diameter of 5 cm, though bend diameters as small as 1.5 cm,or even smaller, may be used without inhibiting mode-locking. Due to theEr³⁺ doping, the fiber core in this example has an absorption ofapproximately 40 dB/m at a wavelength of 1.53 μm. The Yb³⁺ co-dopingproduces an average absorption of 4.3 dB/m inside the cladding at awavelength of 980 nm. The fiber 13 has a numerical aperture of 0.20 anda core diameter of 16 μm. The outside diameter of the cladding of thefiber 13 is 200 μm. The fiber 13 is coated with a low-index polymerproducing a numerical aperture of 0.40 for the cladding. A 10 cm lengthof single-mode Coming Leaf fiber 15 is thermally tapered to produce acore diameter of approximately 14 μm to ensure an optimum operation as amode filter, and this length is fusion spliced onto a first end 17 ofthe multi-mode fiber 13.

In this exemplary embodiment, the cavity 11 is formed between a firstmirror 19 and a second mirror 21. It will be recognized that othercavity configurations for recirculating pulses are well known, and maybe used. In this example, the mirrors 19, 21 define an optical axis 23along which the cavity elements are aligned.

The cavity 11 further includes a pair of Faraday rotators 25, 27 tocompensate for linear phase drifts between the polarization eigenmodesof the fiber, thereby assuring that the cavity remains environmentallystable. As referenced herein, the phrase “environmentally stable” refersto a pulse source which is substantially immune to a loss of pulsegeneration due to environmental influences such as temperature driftsand which is, at most, only slightly sensitive to pressure variations.The use of Faraday Rotators for assuring environmental stability isexplained in more detail in U.S. Pat. No. 5,689,519 which has beenincorporated by reference herein.

A polarization beam-splitter 29 on the axis 23 of the cavity 11 ensuressingle-polarization operation of the cavity 11, and provides the output30 from the cavity. A half-wave plate 31 and a quarter-wave plate 33 areused to introduce linear phase delays within the cavity, providingpolarization control to permit optimization of polarization evolutionwithin the cavity 11 for mode-locking.

To induce mode-locking, the cavity 11 is formed as a Fabry-Perot cavityby including a saturable absorber 35 at the end of the cavity proximatethe mirror 19. The saturable absorber 35 is preferably grown as a 0.75μm thick layer of InGaAsP on one surface of a substrate. The band-edgeof the InGaAsP saturable absorber 39 is preferably chosen to be 1.56 μm,the carrier life-time is typically 5 ps and the saturation energydensity is 100 MW/cm².

In this example, the substrate supporting the saturable absorber 35comprises high-quality anti-reflection-coated InP 37, with theanti-reflection-coated surface 39 facing the open end of the cavity 11.The InP substrate is transparent to single-photon absorption of thesignal light at 1.56 μm, however two photon absorption occurs. Thistwo-photon absorber 39 is used as a nonlinear power limiter to protectthe saturable absorber 35.

The mirror 19 in this exemplary embodiment is formed by depositing agold-film onto the surface of the InGaAsP saturable absorber 35 oppositethe two photon absorber 39. The combined structure of the saturableabsorber 35, two photon absorber 37 and mirror 19 provides areflectivity of 50% at 1.56 μm. The surface of the gold-film mirror 19opposite the saturable absorber 35 is attached to a sapphire window 41for heat-sinking the combined absorber/mirror assembly.

The laser beam from the fiber 15 is collimated by a lens 43 andrefocused, after rotation by the Faraday rotator 25, by a lens 45 ontothe anti-reflection-coated surface 39 of the two-photon absorber 37. Thespot size of the laser beam on the saturable absorber 35 may be adjustedby varying the position of the lens 45 or by using lenses with differentfocal lengths. Other focusing lenses 47 and 49 in the cavity 11 aid inbetter imaging the laser signal onto the multi-mode fiber 13.

Light from a Pump light source 51, such as a laser source, with awavelength near 980 nm and output power of 5 W, is directed through afiber bundle 57 with an outside diameter of 375 μm. This pump light isinjected into the end 53 of the multi-mode fiber 13 opposite thesingle-mode fiber 17. The pump light is coupled into the cavity 11 via apump signal injector 55, such as a dichroic beam-splitter for 980/1550nm. Lenses 47 and 48 are optimized for coupling of the pump power fromthe fiber bundle 57 into the cladding of the multi-mode fiber.

The M²-value of the beam at the output 30 of this exemplary embodimentis typically approximately 1.2. Assuming the deterioration of theM²-value is mainly due to imperfect splicing between the multi-modefiber 13 and the single-mode mode-filter fiber 15, it can be estimatedthat the single-mode mode-filter fiber 15 excited the fundamental modeof the multi-mode fiber 13 with an efficiency of approximately 90%.

Mode-locking may be obtained by optimizing the focussing of the laserbeam on the saturable absorber 35 and by optimizing the orientation ofthe intra-cavity waveplates 31, 33 to permit some degree of nonlinearpolarization evolution. However, the mode-locked operation of amulti-mode fiber laser system without nonlinear polarization evolutioncan also be accomplished by minimizing the amount of mode-mixing in themulti-mode fiber 13 and by an optimization of the saturable absorber 35.

The pulses which are generated by the exemplary embodiment of FIG. 1will have a repetition rate of 66.7 MHz, with an average output power of300 mW at a. wavelength of 1.535 μm, giving a pulse energy of 4.5 nJ. Atypical autocorrelation of the pulses is shown in FIG. 2. A typical FWHMpulse width of 360 fsec (assuming a sech² pulse shape) is generated. Thecorresponding pulse spectrum is shown in FIG. 3. The autocorrelationwidth is within a factor of 1.5 of the bandwidth limit as calculatedfrom the pulse spectrum, which indicates the relatively high quality ofthe pulses.

Due to the multi-mode structure of the oscillator, the pulse spectrum isstrongly modulated and therefore the autocorrelation displays asignificant amount of energy in a pulse pedestal. It can be estimatedthat the amount of energy in the pedestal is about 50%, which in turngives a pulse peak power of 6 KW, about 6 times larger than what istypically obtained with single-mode fibers at a similar pulse repetitionrate.

Neglecting the amount of self-phase modulation in one pass through themulti-mode fiber 13 and any self-phase modulation in the mode-filter 15,and assuming a linear increase of pulse power in the multi-mode fiber 13in the second pass, and assuming an effective fundamental mode area inthe multi-mode fiber 13 of 133 μm², the nonlinear phase delay in themulti-mode oscillator is calculated from the first equation above asΦ_(nl)=1.45π, which is close to the expected maximum typical nonlineardelay of passively mode-locked lasers.

The modulation on the obtained pulse spectrum as well as the amount ofgenerated pedestal is dependent on the alignment of the mirror 21.Generally, optimized mode-matching of the optical beam back into thefundamental mode of the multi-mode fiber leads to the best laserstability and a reduction in the amount of pedestal and pulse spectrummodulation. For this reason, optimized pulse quality can be obtained byimproving the splice between the single-mode filter fiber 15 and themulti-mode fiber 13. From simple overlap integrals it can be calculatedthat an optimum tapered section of Coming SMF-28 fiber 15 will lead toan excitation of the fundamental mode in the multi-mode fiber 13 with anefficiency of 99%. Thus any signal in higher-order modes can be reducedto about 1% in an optimized system.

An alternate embodiment of the invention is illustrated in FIG. 4. Asindicated by the identical elements and reference numbers, most of thecavity arrangement in this figure is identical to that shown in FIG. 1.This embodiment provides a highly integrated cavity 59 by employing aside-pumping mechanism for injecting pump light into the multi-modefiber 13. A pair of fiber couplers 61, 63, as are well known in the art,inject light from a respective pair of fiber bundles 65 and 67 into thecladding of the multi-mode fiber 13. The fiber bundles are similar tobundle 57 shown in FIG. 1, and convey light from a pair of pump sources69 and 71, respectively. Alternatively, the fiber bundles 65, 67 andcouplers 61, 63 may be replaced with V-groove light injection into themulti-mode fiber cladding in a manner well known in the art. A saturableabsorber 73 may comprise the elements 35, 37, 39 and 41 shown in FIG. 1,or may be of any other well known design, so long as it provides a highdamage threshold.

In another alternate embodiment of the invention, Illustrated in FIG. 5,the laser cavity 75 includes a positive dispersion element. As With FIG.4, like reference numbers in FIG. 5 identify elements described indetail with reference to FIG. 1. In this embodiment, a section ofsingle-mode positive dispersion fiber 77 is mounted between the secondmirror 21 and the lens 49. In a similar manner, a section of positivedispersion fiber could be spliced onto the end 53 of the multi-modefiber 13, or the end of the single-mode mode-filter 15 facing the lens43. Positive dispersion fibers typically have a small core area, and maylimit the obtainable pulse energy from a laser. The embodiment shown inFIG. 5 serves to reduce the peak power injected into the positivedispersion fiber 77, and thus maximize the pulse energy output. This isaccomplished by extracting, at the polarization beam splitter 29, asmuch as 90-99% of the light energy.

In the embodiment of FIG. 5, the total dispersion inside the cavity maybe adjusted to be zero to generate high-power pulses with a largerbandwidth. Alternatively, by adjusting the total cavity dispersion to bepositive, chirped pulses with significantly increased pulse energies maybe generated by the laser.

The use of two single-mode mode-filter fibers 15, 77 is also beneficialin simplifying the alignment of the laser. Typically, to minimize modalspeckle, broad bandwidth optical signals need to be used for aligningthe mode-filter fibers with the multi-mode fiber. The use of twomode-filter fibers 15, 77 allows the use of amplified spontaneousemission signals generated directly in the multi-mode fiber for aniterative alignment of both mode-filters 15, 77.

The chirped pulses generated in the cavity 75 with overall positivedispersion may be compressed down to approximately the bandwidth limitat the frequency doubled wavelength by employing chirped periodicallypoled LiNbO₃ 79 for sum-frequency generation, in a manner well known inthe art. The chirped periodically poled LiNbO₃ 79 receives the cavityoutput from the polarization beam splitter 29 through an opticalisolator 81. In this case, due to the high power capabilities ofmulti-mode fiber oscillators, higher frequency-doubling conversionefficiencies occur compared to those experienced with single-mode fiberoscillators. Alternatively, bulk-optics dispersion compensating elementsmay be used in place of the chirped periodically poled LiNbO₃ 79 forcompressing the chirped pulses down to the bandwidth limit.

Generally, any nonlinear optical mixing technique such as frequencydoubling, Raman generation, four-wave mixing, etc. may be used in placeof the chirped periodically poled LiNbO₃ 79 to frequency convert theoutput of the multi-mode oscillator fiber 13 to a different wavelength.Moreover, the conversion efficiency of these nonlinear optical mixingprocesses is generally proportional to the light intensity or lightintensity squared. Thus, the small residual pedestal present in amulti-mode oscillator would be converted with greatly reduced efficiencycompared to the central main pulse and hence much higher quality pulsesmay be obtained.

As shown in the alternate embodiment of FIG. 6, very high-energy opticalpulses may also be obtained by inserting a chirped fiber grating such asa Bragg grating 83, with negative dispersion, into the cavity 85. Such asystem typically produces ps length, high-energy, approximatelybandwidth-limited pulses. Due to the multi-mode fiber used, much greaterpeak powers compared to single-mode fiber oscillators are generated.Here the fiber grating 83 is inserted after the polarization beamsplitter 29 to obtain an environmentally-stable cavity even in thepresence of nonpolarization maintaining multi-mode fiber 13.

In each of the embodiments of this invention, it is advantageous tominimize saturation of the multi-mode fiber amplifier 13 by amplifiedspontaneous emission generated in higher-order modes. This may beaccomplished by confining the rare-earth doping centrally within afraction of the core diameter.

Polarization-maintaining multi-mode optical fiber may be constructed byusing an elliptical fiber core or by attaching stress-producing regionsto the multi-mode fiber cladding. Examples of such fiber cross-sectionsare shown in FIGS. 7 a and 7 b, respectively. Polarization-maintainingmulti-mode fiber allows the construction of environmentally stablecavities in the absence of Faraday rotators. An example of such a designis shown in FIG. 8 in this case, the output of the cavity 87 is providedby using a partially-reflecting mirror 89 at one end of the cavity 87,in a manner well known in this art.

To ensure optimum matching of the fundamental mode of the multi-modefiber 13 to the mode of the single-mode mode-filter fiber 15 in each ofthe embodiments of this invention, either a bulk optic imaging system, asplice between the multi-mode fiber 13 and the single-mode fiber 15, ora tapered section of the multi-mode fiber 13 may be used. For example,the multi-mode fiber 13, either in the form shown in one for FIG. 7 aand FIG. 7 b or in a non-polarization maintaining form may be tapered toan outside diameter of 70 μm. This produces an inside core diameter of5.6 μm and ensures single mode operation of the multi-mode fiber at thetapered end. By further employing an adiabatic taper, the single-mode ofthe multi-mode fiber may be excited with nearly 100% efficiency. Agraphic representation of the three discussed methods for excitation ofthe fundamental mode in an multi-mode fiber 13 with a single-mode fibermode-filter 15 is shown in FIGS. 9 a, 9 b and 9 c, respectively. Theimplementation in a cavity design is not shown separately, but thesplice between the single-mode fiber 15 and the multi-mode fiber 15shown in any of the disclosed embodiments may be constructed with any ofthe three alternatives shown in these figures.

FIG. 10 shows an additional embodiment of the invention. Here, insteadof single-mode mode-filter fibers 15 as used in the previousembodiments, fiber gratings such as a Bragg grating directly writteninto the multi-mode fiber 13 is used to predominantly reflect thefundamental mode of the multi-mode fiber 13. Light from the pump 51 isinjected through the fiber grating 97 to facilitate a particularlysimple cavity design 99. Both chirped fiber gratings 97 as well asunchirped gratings can be implemented. Narrow bandwidth (chirped orunchirped) gratings favor the oscillation of pulses with a bandwidthsmaller than the grating bandwidth.

Finally, instead of passive mode-locking, active mode-locking oractive-passive mode-locking techniques may be used to mode-lockmulti-mode fibers. For example, an active-passive mode-locked systemcould comprise an optical frequency or amplitude modulator (as theactive mode-locking mechanism) in conjunction with nonlinearpolarization evolution (as the passive mode-locking mechanism) toproduce short optical pulses at a fixed repetition rate without asaturable absorber. A diagram of a mode-locked multi-mode fiber 13 witha optical mode-locking mechanism 101 is shown in FIG. 11. Also shown isan optical filter 103, which can be used to enhance the performance ofthe mode-locked laser 105.

Generally, the cavity designs described herein are exemplary of thepreferred embodiments of this invention. Other variations are obviousfrom the previous discussions. In particular, optical modulators,optical filters, saturable absorbers and a polarization control elementsare conveniently inserted at either cavity end. Equally, output couplingcan be extracted at an optical mirror, a polarization beam splitter oralso from an optical fiber coupler attached to the single-mode fiberfilter 15. The pump power may also be coupled into the multi-mode fiber13 from either end of the multi-mode fiber 13 or through the side of themulti-mode fiber 13 in any of the cavity configurations discussed.Equally, all the discussed cavities may be operated with any amount ofdispersion. Chirped and unchirped gratings may be implemented at eithercavity end to act as optical filters and also to modify the dispersioncharacteristics of the cavity.

FIG. 12 illustrates an amplifier system according to a first embodimentof the present invention. In the example shown in FIG. 12, a femtosecondsingle-mode (SM) fiber oscillator 1010, such as an erbium fiberoscillator, is coupled into a multi-mode (MM) fiber amplifier 1012, suchas an erbium/ytterbium fiber amplifier. Other examples of suitable MMfiber amplifiers include those doped with Er, Yb, Nd, Tm, Pr or Ho ions.Oscillators suitable for use in this system are described in theabove-mentioned U.S. patent application Ser. No. 08/789,995 to Fermannet al.

A two-lens telescope 14 (L1 and L2) is used to match the mode from theoscillator 1010 to the fundamental mode of the MM amplifier 1012. Inaddition, the output of the pumped MM fiber 1012 is imaged into a secondSM fiber (mode-filter (MF) fiber 1016 in FIG. 12) using lenses L3 andL4. Lenses L3 and L5 and beamsplitter 1018 are used to couple the pumplight from pump source 1020 into the amplifier fiber, as describedbelow.

In one example of the system arranged according to FIG. 12, theoscillator 1010 delivers 300 fsec near bandwidth-limited pulses at arepetition rate of 100 MHz at a wavelength of 1.56 μm with a power levelof 14 mW.

The amplifier fiber 12 can be, for example, a double-clad MMerbium/ytterbium amplifier with a core diameter of ≈28 μm and a corenumerical aperture of NA=0.19. The inner cladding in this example has adiameter of ≈220 μm and a numerical aperture of NA=0.24. The core islocated in the center of the inner cladding. The length of the amplifieris 1.10 m.

To increase the number of propagating modes in the MM amplifier 1012 andfor testing purposes, shorter wavelengths such as 780 and 633 nm werealso used. In this, a femto-second laser source operating at 780 nm anda cw laser source at 633 nm can be launched into the MM amplifier fiber1012. The MF fiber 1016 can then be replaced with a fiber with a corediameter of 4 μm to ensure SM operation at these two wavelengths.

The approximate number of modes in the MM amplifier is calculated fromits V-value. $\begin{matrix}{{v = {\frac{2\pi\quad a}{\lambda}{NA}}},\quad{{{number}\quad{of}\quad{modes}} = {\frac{1}{2}v^{2}}}} & (1)\end{matrix}$where a is the core radius and λ is the signal wavelength. The V-valueat 1.55 μm is thus V≈10.8, and the number of modes is hence calculatedas ≈58 for the above example. Typically, a fiber is considered MM whenthe V-value exceeds 2.41, i.e., when modes in addition to thefundamental mode can propagate in the optical fiber.

For equal excitation of N modes of a MM fiber supporting N modes themaximum coupling efficiency into a SM fiber is given approximately byη≈(θ₀/θ_(max))²≈1/N,  (2)where θ₀≈λ/4a is the divergence half-angle of the fundamental mode ofthe MM fiber. θ_(max) is the maximum divergence half-angle of theouter-most modes of the MM fiber. It is assumed that the output from theMM fiber is linearly polarized which is an appropriate assumption forthe excitation of the lowest order modes in the fiber. Under SMexcitation of the MM fiber and in the absence of mode-coupling,θ_(max)(Z)−θ₀ independent of fiber length. However, in the presence ofmode-coupling θ_(max) will increase, and, as a result, the possiblecoupling efficiency from the output of the MM fiber into a SM fiber willdecrease as η(z)=(θ₀/θ_(max)(z))². Using the above-mentioned work byGloge, η(z) can be written as: $\begin{matrix}{{\eta(z)} = \frac{\theta_{0}^{2}}{{4{Dz}} + \theta_{0}^{2}}} & (3)\end{matrix}$where D is the mode-coupling coefficient as defined by Gloge. Thus, ameasurement of η(z) gives the mode-coupling coefficient D. Equally, fromequation (2), a measurement of η gives the approximate number of excitedmodes of a MM fiber. It is instructive to relate N to the M²-value thatis typically used to characterize the quality ofnear-diffraction-limited optical beams. It may be shown that N≈{squareroot}{square root over (M²)}. According to the present invention, a lowlevel of mode-coupling is desirable, so that the amplified beam providedat the output of the MM fiber amplifier 1012 is substantially in thefundamental mode. Accordingly, an M²-value less than 10 is desirable,with an M²-value less than 4 being preferable, and an M²-value less than2 being more preferable. Further, the number of modes is preferably inthe range of 3 to 3000 and more preferably in the range of 3 to 1000.

Mode-coupling was measured in a 1.1 m length of unpumped amplifier fiberfor the above-described erbium/ytterbium fiber (fiber 1), and threecommercially available MM-fibers (fiber 2, 3 and 4). The fiberparameters and the mode-coupling coefficient D (in m⁻¹) of these fibersare shown in Table 1. Fibers 1, 3 and 4 are made by the MCVD process;fiber 2 is made by a rod-in-tube technique. TABLE 1 fiber 1 fiber 2fiber 3 fiber 4 NA 0.19 0.36 0.13 0.13 core diameter (μm) 28 50 50 50cladding diameter 200 125 125 250 (μm) number of modules at 58 665 87 871.55 μm number of modes at 223 0.79 μm number of modes at 330 0.63 μmD(m⁻¹) at 1.55 μm <2 × 10⁻⁶ 8 × 10⁻⁴ 8 × 10⁻⁵ 7 × 10⁻⁶ D(m⁻¹) at 0.79 μm  4 × 10⁻⁶ D(m⁻¹) at 0.63 μm   2 × 10⁻⁵ L_(b)(mm) at 1.55 μm 1.9 5.3 5.75.7 L_(b)(mm) at 0.79 μm 3.3 L_(b)(mm) at 0.63 μm 4.1 M²(1 m) at 1.55 μm1.0 200 5.4 1.25 M²(1 m) at 0.79 μm 1.2 M²(1 m) at 0.63 μm 2.6

The coupling coefficients allow, in turn, the calculation of theexpected M² value. In this example, the calculated M²-values wereproduced after propagation through 1 m of MM fiber 1012. For fiber 1, agood agreement between the calculated and separately measured M²-valueswas obtained.

The beat length L_(b) between the fundamental LP₀₁ and the nexthigher-order LP₁₁ mode is also given in Table 1. The beat length L_(b)is defined as the length it takes for the two modes to accumulate adifferential phase-shift of 2π along the propagation direction. Assuminga constant scattering power spectrum, for a fixed wavelength, D can beshown to be proportional to L_(b) ⁴.

See: D. Marcuse, “The Theory of Dielectric Optical Waveguides”, p. 238,Academic Press (1974); Gloge. The longer the beat length, the closer themodes are to being phase-matched and the more power will couple as afunction of length. Since, as disclosed by Gloge, mode-coupling isexpected to be largest between adjacent modes, it is desirable to useLP₀₁/LP₁₁ beat lengths as short as possible to avoid mode-coupling.

In general, high levels of mode-coupling can be expected from fiberswith high scattering loss. This suggests the possibility of lowmode-coupling coefficients at long wavelengths in fibers with lowscattering loss. As can be seen from Table 1, a dramatic reduction ofmode-coupling occurs with increased wavelength in fiber 1. An acceptablelevel of mode-coupling is achieved in fiber 1 down to wavelengths asshort as 790 nm. Since the number of modes of an optical fiber dependsonly on the ratio a/λ, a fiber similar to fiber 1 with a core diameteras large as 56 μm can produce acceptable levels of mode-coupling in a 1m length. Due to the reduction of scattering at longer wavelengths, evenlarger core diameters are acceptable at longer wavelengths. For example,a MM fiber with a core diameter of 60 μm can amplify pulses with a peakpower 16 times larger than possible with SM amplifiers described byTaverner et al. Indeed, acceptable levels of mode coupling were obtainedfor a specifically designed fiber with a 50 μm core diameter as evidentfrom Table 1 and explained in the following.

Further, it is clear that, to minimize mode-coupling, step-index MMfibers are more useful than graded-index MM fibers, since thepropagation constants in graded-index fibers are very similar, whichgreatly increases their sensitivity to mode coupling. To minimizemode-coupling, the difference in the propagation constants between fibermodes is preferably maximized.

Fiber 2 was manufactured by a rod-in-tube technique with intrinsic highscattering losses leading to much larger mode-coupling coefficientscompared to the MCVD-grown fibers 1, 3 and 4. Also, the mode-couplingcoefficients measured in fiber 2 are similar to results obtained byGambling et al. and Griebner et al., who also used step-index solid-corefibers manufactured by rod-in-tube techniques. As a consequence, reducedmode-coupling can be expected from directly grown MM fibers employing,for example, MCVD, OVD, PCVD or VAD fiber fabrication techniques.

As shown in Table 1, the mode-coupling coefficients obtained in fiber 4at 1.55 μm are about a factor of 11 smaller than in fiber 3. Thisdifference is explained by the fact that the outside diameter of fiber 4is 250 μm, whereas the outside diameter of fiber 3 is 125 μm. Ingeneral, a thicker fiber is stiffer and less sensitive to bend andmicro-bend induced mode-coupling, as evident from Table 1.

In experiments conducted by the inventors, the lowest mode-couplingcoefficients were obtained by longitudinally stretching the opticalfibers. For example, the mode-scattering coefficients of fiber 2 and 3were measured while keeping the fiber under tension and while keepingthe fiber straight. The application of tension in short lengths offibers can be useful in obtaining the best possible mode-quality.

Mode-coupling was also measured in a configuration where the amplifierfiber (fiber 1) was pumped, as shown in FIG. 12. Specifically, theamplifier was pumped at a wave-length of 980 nm contra-directionallywith respect to the signal with a launched power up to 3 W from abroad-stripe semiconductor laser with an active area of 1×500 μm, wheredemagnification was employed to optimize the power coupling into theinner cladding of the MM amplifier fiber. The amplifier was cleaved atan angle of about 8° to eliminate spurious feedback. A signal power upto 100 mW was then extracted from the amplifier system at 1.56 μm.

The coupling efficiency of the MM amplifier fiber 1012 into the MF fiber1016 as a function of bend-radius of the MM amplifier fiber 1012 isshown in FIG. 13. For a straight MM amplifier fiber and for abend-radius of 10 cm, a coupling efficiency up to 94% is obtained intothe MF fiber 1016, demonstrating that mode-coupling is nearly completelyabsent in the MM amplifier fiber 1012 and that a SM can indeed propagateover lengths of several meters in such fibers. No clear onset ofmode-coupling is visible even for a bend-radius of 5 cm, since, even inthis case, a coupling efficiency of about 90% from the MM amplifierfiber 1012 to the MF fiber 1016 is obtained.

Since the measured coupling efficiencies from the MM amplifier 1012 to aSM fiber are nearly the same under unpumped and pumped conditions, it isevident that gain-guiding is relatively weak in this particularamplifier fiber. This observation was also verified by a simple computermodel (see below). However, clearly any dopant confinement in the centerof the MM amplifier core will predominantly lead to amplification of thefundamental mode. Any light scattered into higher-order modes willexperience less gain and, due to the reduced intensity overlap of thehigher-order modes with the fundamental mode, low levels of scatteredlight in higher-order modes will also not saturate the gain of thefundamental mode. Thus, while in the above-described experimentalexample, the mode-scattering coefficients were so low that any effectsdue to gain-guiding were not readily observable, in general,gain-guiding plays a role in a MM amplifier system according to thepresent invention. In addition, the above-mentioned computer modelpredicts the onset of gain-guiding of the fundamental mode in MM fiberswith larger core diameter and/or reduced refractive index differencesbetween the core and cladding.

As the mode diameter increases, the size of the SM can be determined bythe gain profile under small signal conditions, i.e. in the absence ofgain saturation. This allows a length-dependent mode size. Initially,under small signal conditions, the mode is confined by gain-guiding. Asthe gain saturates, gain guiding becomes less relevant and the mode sizecan increase, limited eventually by the core of the MM fiber. Alength-dependent mode size can also be achieved by employing a core sizewhich tapers along the fiber length. This can, for example, be achievedby tapering the outside fiber diameter along the fiber length.

In the presence of gain-guiding, amplified spontaneous emission (ASE) isreduced, as the MM fiber essentially becomes SM. In the presence ofgain-guiding, ASE is also guided predominantly in the fundamental mode,rather than in all possible modes of the MM fiber, leading to animprovement in the noise properties of the MM fiber.

Equally, in the experimental example, dopant-confinement was observed tolead to a significant reduction in the amplified spontaneous emission(ASE) levels in the fiber. This was verified by measuring the couplingefficiency of the ASE from the MM amplifier 1012 into the MF fiber 1016.In this case, no signal light was coupled into the MM amplifier fiber1012. For an ASE power level of 1 mW, a coupling efficiency as high as15% was measured. A comparison with equation (2) indicates that ASE isgenerated mainly in about 13 low-order modes (here a factor of two frompolarization degeneracy is accounted for), i.e., ASE is generated inonly about 20% of the total mode-volume of the amplifier fiber. Thelarge reduction in ASE which was observed not only reduces the noiselevel in the amplifier; low levels of ASE also allow a reduction of thesignal power that is required to saturate the amplifier. To extract thehighest energy from an oscillator-amplifier signal pulse source, anoperation of the amplifier in saturation is generally preferred.

The coupling efficiency at 1.55 μμm and at 780 nm from the MM amplifierfiber 1012 to the MF fiber 1016 was not found to vary when applyingsmall mechanical perturbations to the optical fiber. In a practicaloptical system, the applied mechanical perturbations are small comparedto the perturbations inflicted by a 5 cm bend radius, which indicatesthat long-term stability of the mode-propagation pattern in such fiberscan be achieved.

The MM amplifier 1012 is polarization preserving for bend-radii as smallas 10 cm. To obtain a high-degree of polarization holding, ellipticalfiber cores or thermal stresses can be used in such fibers.

The autocorrelation of the amplified pulses from the MM amplifier fiber1012 (bend radius=10 cm) measured under the condition of optimummode-match and a condition of non-optimum mode-match are respectivelyshown in FIGS. 14 and 15. Under non-optimum mode-match, theautocorrelation displays several peaks due to the excitation ofhigher-order modes, which have different propagation constants. However,under optimum mode-matching conditions, any secondary peaks aresuppressed to better than 1%, which indicates the high-quality of thepulses emerging from the MM amplifier fiber.

In general, the spectrum of the pulses measured at the output of the MMamplifier fiber 1012 is more critically dependent on the couplingconditions than the autocorrelation. The reason for this is that thespectral measurement is sensitive to the phase between the fundamentalmode and the higher-order modes, i.e., an energy content of higher-ordermodes of only 1% in the output of the MM fiber leads to a perturbationof the shape of the spectrum by 10%.

FIG. 16 is a block diagram of a multi-mode fiber amplifier systemaccording to a second embodiment of the present invention. The systemincludes a near-diffraction limited input beam, a mode-converter 1050and a MM fiber amplifier 1052. The near-diffraction limited input beamcan be generated from any laser system, which need not be a fiber laser.The near-diffraction limited input beam can contain cw or pulsedradiation. The mode-converter 1050 can consist of any type of opticalimaging system capable of matching the mode of the MM amplifier 1052.For example, a lens system may be employed. Alternatively, a section oftapered fiber may be employed, such that the output mode at the end ofthe tapered fiber is matched to the mode of the MM amplifier fiber 1052.In this case, the mode-converter can be spliced directly to the MM fiber1052 producing a very compact set-up. Any pumping configuration could beemployed for the MM amplifier fiber, such as contra- or co-directionalpumping with respect to the signal or side-pumping. Equally, the NA ofthe pump light could be reduced to minimize ASE. In this case, the useof just a single-clad fiber is more advantageous, where the pump lightis directed into the fiber core. In general, the MM amplifier 1052 canhave a single, double or multiple cladding.

In the case of co-directional pumping, the pump light and the signallight are launched via a dichroic beamsplitter (not shown). The couplingoptics are then optimized to simultaneously optimize the coupling of thepump beam and the signal beam.

A single or a double pass of the signal through the MM fiber 1052 ismost convenient. In the case of a double-pass configuration, a Faradayrotator mirror can be employed to eliminate polarization drifts in thesystem. Of course, in a double-pass configuration, after the first passthrough the amplifier the coupling of the signal into higher-order modesmust be avoided to ensure a near-diffraction limited output.

Optionally, linear or nonlinear optical elements can be used at theoutput of the system. Such a system is compatible with any applicationthat has been used in conjunction with conventional laser systems.

Many nonlinear applications indeed require high peak pulse powers fortheir efficient operation, which are very difficult to achieve incladding-pumping SM amplifiers due to the 10s of meters of fiber lengththat are typically employed in such systems. Even in standard SM opticalamplifiers, peak powers greater than 1 kW/amplifier length can rarely beachieved. In contrast, peak powers of ≈15 kW are achievable in a 1.5 mlength of double-clad Er/Yb fiber (fiber 1 from Table 1) withoutappreciable non-linear effects, i.e., peak powers greater than 20kW/amplifier length can be achieved.

According to the present invention, the use of a MM amplifier isbeneficial not only by way of allowing the use of a large core diameter;the use of a MM amplifier also allows a reduction of the ratiocladding/doped core diameter, which minimizes the amplifier length andthus the amplifier non-linearity. However, this leads to the generationof more ASE noise.

FIG. 17 is a block diagram illustrating a multi-mode fiber amplifiersystem according to a third embodiment of the present invention. In thesystem of the third embodiment, high-power optical pulses can bepropagated (or amplified) in undoped (or amplifier) MM fibers, such thatspectral broadening is obtained to allow for pulse compression of theamplifier output. For applications in nonlinear pulse-compression,optical fibers with either positive (non-soliton-supporting) or negative(soliton-supporting) dispersion can be employed. The power levels in themulti-mode fiber 1060 are raised to obtain an appreciable amount ofself-phase modulation. The interplay of dispersion and self-phasemodulation in the optical fiber can then be used to broaden the spectrumof the optical pulses and to obtain pulse compression.

When the MM fiber 1060 is soliton supporting, higher-order solitoncompression may be used to produce short pulses from the MM fiber 1060directly. In general, in the case of positive dispersion (non-solitonsupporting) fiber, additional linear or nonlinear pulse-compressioncomponents must be used to compress the spectrally broadened opticalpulses. In this case, a conventional linear pulse compressor 1062 (suchas a prism, grating, grism or SM chirped fiber Bragg grating) may beused at the output of the system. Also, chirped periodically poleddoubling crystals may be used to obtain a compressed, frequency-doubledpulse. Equally, chirped fiber Bragg gratings may be written into the MMoptical fiber 1060 with reduced mode-coupling to reduce thenonlinearities of such structures when applied to linear pulsecompressor 1062. The Bragg grating should not be blazed to eliminate theexcitation of higher-order modes in reflection.

FIG. 18 is a diagrammatic view of a system according to a fourthembodiment of the present invention. As shown in FIG. 18, a mode-filter1070 is inserted in front of one of the cavity mirrors M1 and M2 toensure a diffraction-limited output of the system. The mode filter 1070can consist of a standard SM fiber in conjunction with appropriatemode-matching optics. Alternatively, a tapered fiber can be used (asdiscussed above) to provide for mode-matching. For optimum mode-couplingthe efficiency of the laser will be nearly as high as for an all-SMlaser. However, the use of MM amplifier 1076 allows for increased designflexibility. Thus, double-clad erbium/ytterbium fibers with differentcore-cladding ratios can be employed wherever appropriate.

According to a fifth embodiment, the use of MM fiber allows the designof double-clad fibers with low absorption cross sections. For example, adouble-clad Er-doped amplifier fiber may be constructed from MM fibers.Typically Er-doped double-clad fibers are relatively inefficient, sincelarge cladding/core ratios have to be employed in order to absorb pumplight from broad area diode lasers while still preserving a SM fibercore. Typically, such a design would involve a Φ_(cl)=100 μm diametercladding and a Φ_(co)=10 μm diameter core. The effective absorption ofsuch a structure is 100 times (=Φ_(cl)/Φ_(co))² smaller than theabsorption in a single-clad Er-doped fiber. Thus, 100 times longer fiberamplifier lengths are required in this case. However, by implementing MMEr-doped fiber, the core size can be greatly increased, producing muchsmaller cladding/core ratios and shorter amplifier lengths which is verybeneficial for the design of high-power lasers. Of course, for thedesign of high-power Er double-clad lasers, cladding diameters evenlarger than 100 μm can be implemented. A conceptual drawing of a fibercross section employing a doped MM fiber core and an undoped fibercladding is shown in FIG. 19. As shown in FIG. 19, the active dopant isconfined in a cross section, defined by the dopant profile,substantially smaller than the fiber core, as defined by the refractiveindex profile. Of course, in such laser system, dopant confinementincreases the amplifier length, thus only relatively weak dopingconfinement is useful.

According to a sixth embodiment of the present invention, as shown nFIG. 20, a fiber regenerative amplifier may be constructed from a MMfiber amplifier 1090. A regenerative amplifier is useful for obtainingmJ energies from MM fiber amplifiers. Due to the limited gain of MMfiber amplifiers, the extraction of mJ energies will typically requireseveral passes through the amplifier, which is facilitated by theregenerative amplifier. As shown in FIG. 20, a fast optical switch (OS)1092 is used to switch the pulses in and out of the regenerativeamplifier. A mode-filter 1094 can also be included to “clean-up” thefiber mode in the amplification process. The mode-filter 1094 canconsist of a spatial filter to minimize any nonlinearities in theregenerative amplifier.

The seed pulse is selected from the oscillator 1096 by the opticalswitch 1092 at the desired repetition rate. The Faraday rotator 1098 andthe polarization beam splitter 1099 are used to couple the amplifiedpulse out of the system.

Either cw or pulsed pumping of the amplifier can be employed.

According to a seventh embodiment of the present invention shown in FIG.21, a MM Q-switched fiber laser source is constructed. The largecross-sections possible with MM fibers allow greatly increasing theenergy storage compared to a single-mode fiber. As a result, high-powerQ-switched pulses may be directly generated from such a system.Typically, these pulses have a duration in the nsec regime. As shown inFIG. 21, a mode-filter 10100 can also be included to ensure an optimummode-quality. The optical switch 10102 is employed for output couplingand it also serves to modulate the loss (Q) of the cavity defined by thetwo mirrors M1 and M2 and the MM amplifier 10104. Alternatively, theoutput can be extracted by using a partially transmissive mirror M2.

According to an eighth embodiment of the present invention shown in FIG.22, a preamplifier is included in front of the final MM amplifier fiber10112 to fully saturate the MM amplifier fiber 10112 and to reduce thelevel of ASE in the MM amplifier fiber 10112. The preamplifier can be SMand also MM, where it is useful to select the core radius of thepreamplifier fiber 10110 to be smaller than the core radius of the finalMM amplifier fiber 10112 to minimize the growth of ASE. One isolator(not shown) can be inserted between the laser source and thepreamplifier and another isolator (not shown) can be inserted betweenthe preamplifier 10110 and the final MM amplifier fiber 10112 further toreduce ASE. Similarly, narrow band optical filters (not shown) can beincluded anywhere in the system to reduce ASE. Also, optical switches(not shown) can be used in between the laser source, the preamplifier10110 and the final amplifier 10112 to reduce the amount of ASE.

More than one preamplifier can be used in the system, where isolatorsand optical filters and optical switches can be used to minimize theamount of generated ASE in the system. Further, nonlinear processes inthe preamplifiers and the final MM amplifier can be used for pulsecompression.

According to a ninth embodiment of the present invention shown in FIG.23, a frequency converter 10120 is included downstream of the MMamplifier fiber 10122 to frequency convert the output amplified beam.The frequency converter can be a non-linear crystal, such as aperiodically-poled or a periodically poled LiNbO₃ crystal whichfrequency doubles the output beam.

Although several exemplary embodiments have been herein shown anddescribed, those of skill in the art will recognize that manymodifications and variations are possible without departing from thespirit and scope of the invention, and it is intended to measure theinvention only by the appended claims.

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 59. A multi-mode fiberamplifier system providing discrimination between a fundamental mode andundesired higher-order modes, said amplifier system comprising: a lightsource for producing a light beam, and a linear multi-mode fiberamplifier for receiving said light beam and comprising a multi-modedoped optical fiber having a V-number equal to or higher than 2.41 withrespect to an input signal, capable of supporting a fundamental mode andhigher-order modes, having a radius of curvature such that thehigher-order modes of said input signal experience substantiallyincreased bend losses as compared with the fundamental mode of saidinput signal.
 60. An amplifier system according to claim 59 wherein saidfiber comprises a coiled fiber.
 61. An amplifier system according toclaim 60 wherein said coiled fiber has a constant radius of curvature.62. An amplifier system according to claim 59 wherein said light sourcecomprises a continuous wave light source.
 63. An amplifier systemaccording to claim 59 wherein said light source comprises a pulsed lightsource.
 64. An amplifier system according to claim 59 wherein saidmulti-mode optical fiber comprises a double-cladding structure.
 65. Anamplifier system according to claim 59 wherein said multi-mode opticalfiber comprises a core having a diameter of between 28 microns and 50microns.
 66. An amplifier system according to claim 59 wherein saidmulti-mode fiber amplifier has an M² value less than 2.0, where M²=1denotes diffraction-limited beam quality.
 67. An amplifier systemaccording to claim 59 wherein the fiber amplifier is side pumped.
 68. Alinear multi-mode fiber amplifier comprising: a cylindrical supportmember, and a doped multi-mode optical fiber having a V-number equal toor higher than 2.4 with respect to an input signal, capable ofsupporting a fundamental mode and a plurality of higher-order modes,said fiber being wound onto said support with a radius such that saidhigher-order modes of said input signal experience substantiallyincreased bend loss as compared with the fundamental mode of said inputsignal.
 69. An amplifier system according to claim 68 wherein said woundfiber has a constant radius of curvature.
 70. A multi-mode fiberamplifier according to claim 68 wherein said multi-mode optical fibercomprises a double-cladding structure.
 71. A multi-mode fiber amplifieraccording to claim 68 wherein said multi-mode optical fiber comprises acore having a diameter of between 28 μm and 100 μm.
 72. A multi-modefiber amplifier according to claim 68 wherein said multi-mode fiberamplifier has an M² value less than 2.0, where M²=1 denotesdiffraction-limited beam quality.
 73. An amplifier system as in claim68, further comprising a seed beam having a controlled launch conditionfor preferential excitation of the fundamental mode.